Theorem orim2d 796

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim2d	|- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	orim12d 794	1 |- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 716

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  797  orbi2d  798  pm2.82  820  stdcndcOLD  854  pm2.13dc  893  exmid1dc  4313  acexmidlemcase  6045  poxp  6428  fodjuomnilemdc  7435  omniwomnimkv  7458  exmidontriimlem1  7528  indpi  7657  suplocexprlemloc  8036  nneoor  9680  uzp1  9888  maxabslemlub  11892  xrmaxiflemlub  11933  nninfctlemfo  12736  exmidunben  13177  bj-nn0suc  16734  sbthomlem  16805